Rewrite as a simplified fraction. ${3.\overline{41} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 341.4141...\\ 1x &= 3.4141...\end{align*}}$ Subtracting the two equations, we have: ${99x = 338}$ ${x = \dfrac{338}{99}} \text{or} {3 \dfrac{41}{99}}$